Problem: Solve for $x$ and $y$ using elimination. ${-6x+6y = 24}$ ${-5x-5y = -60}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x+30y = 120}$ $-30x-30y = -360$ Add the top and bottom equations together. $-60x = -240$ $\dfrac{-60x}{{-60}} = \dfrac{-240}{{-60}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-6x+6y = 24}\thinspace$ to find $y$ ${-6}{(4)}{ + 6y = 24}$ $-24+6y = 24$ $-24{+24} + 6y = 24{+24}$ $6y = 48$ $\dfrac{6y}{{6}} = \dfrac{48}{{6}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 5y = -60}$ ${y = 8}$